Find the \( n t h \) term of the sequ \[ \text { (i) } 24,12,6,3, \ldots \]
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The given sequence is a geometric sequence where each term is obtained by multiplying the previous term by a common ratio. 1. Identify the first term \(a\) and the common ratio \(r\): - First term \(a = 24\) - Common ratio \(r = \frac{12}{24} = \frac{1}{2}\) 2. The general formula for the \(n\)-th term of a geometric sequence is given by: \[ a_n = a \cdot r^{(n-1)} \] Substituting the known values: \[ a_n = 24 \cdot \left(\frac{1}{2}\right)^{(n-1)} \] Therefore, the \(n\)-th term of the sequence is: \[ a_n = 24 \cdot \left(\frac{1}{2}\right)^{(n-1)} \]